LMFDB - Embedded newform 209.2.e.b.45.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(45,209)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("209.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 14 x^{16} - 11 x^{15} + 130 x^{14} - 92 x^{13} + 629 x^{12} - 276 x^{11} + 2060 x^{10} + \cdots + 9 $ x^18 - x^17 + 14x^16 - 11x^15 + 130x^14 - 92x^13 + 629x^12 - 276x^11 + 2060x^10 - 681x^9 + 3955x^8 - 115x^7 + 4735x^6 + 105x^5 + 2904x^4 + 1230x^3 + 639x^2 + 81x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			45.6
Root			$0.527190 + 0.913120i$ of defining polynomial
Character	$\chi$	$=$	209.45
Dual form			209.2.e.b.144.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.527190 + 0.913120i) q^{2} +(1.63062 + 2.82432i) q^{3} +(0.444141 - 0.769275i) q^{4} +(-0.650102 - 1.12601i) q^{5} +(-1.71929 + 2.97791i) q^{6} -1.25919 q^{7} +3.04535 q^{8} +(-3.81785 + 6.61271i) q^{9} +O(q^{10})$	\(q+(0.527190 + 0.913120i) q^{2} +(1.63062 + 2.82432i) q^{3} +(0.444141 - 0.769275i) q^{4} +(-0.650102 - 1.12601i) q^{5} +(-1.71929 + 2.97791i) q^{6} -1.25919 q^{7} +3.04535 q^{8} +(-3.81785 + 6.61271i) q^{9} +(0.685455 - 1.18724i) q^{10} -1.00000 q^{11} +2.89690 q^{12} +(1.93899 - 3.35842i) q^{13} +(-0.663833 - 1.14979i) q^{14} +(2.12014 - 3.67219i) q^{15} +(0.717196 + 1.24222i) q^{16} +(-1.18292 - 2.04887i) q^{17} -8.05093 q^{18} +(-4.18891 - 1.20541i) q^{19} -1.15495 q^{20} +(-2.05326 - 3.55636i) q^{21} +(-0.527190 - 0.913120i) q^{22} +(-2.15904 + 3.73957i) q^{23} +(4.96581 + 8.60103i) q^{24} +(1.65473 - 2.86608i) q^{25} +4.08886 q^{26} -15.1181 q^{27} +(-0.559258 + 0.968664i) q^{28} +(1.65802 - 2.87177i) q^{29} +4.47087 q^{30} +8.36713 q^{31} +(2.28915 - 3.96492i) q^{32} +(-1.63062 - 2.82432i) q^{33} +(1.24724 - 2.16029i) q^{34} +(0.818603 + 1.41786i) q^{35} +(3.39132 + 5.87395i) q^{36} -5.09048 q^{37} +(-1.10767 - 4.46046i) q^{38} +12.6470 q^{39} +(-1.97979 - 3.42909i) q^{40} +(4.57108 + 7.91735i) q^{41} +(2.16492 - 3.74975i) q^{42} +(-0.197002 - 0.341218i) q^{43} +(-0.444141 + 0.769275i) q^{44} +9.92796 q^{45} -4.55291 q^{46} +(-3.96958 + 6.87551i) q^{47} +(-2.33895 + 4.05118i) q^{48} -5.41444 q^{49} +3.48944 q^{50} +(3.85778 - 6.68187i) q^{51} +(-1.72237 - 2.98323i) q^{52} +(1.53097 - 2.65172i) q^{53} +(-7.97012 - 13.8047i) q^{54} +(0.650102 + 1.12601i) q^{55} -3.83468 q^{56} +(-3.42607 - 13.7964i) q^{57} +3.49637 q^{58} +(2.47475 + 4.28639i) q^{59} +(-1.88328 - 3.26194i) q^{60} +(2.64087 - 4.57412i) q^{61} +(4.41107 + 7.64020i) q^{62} +(4.80740 - 8.32666i) q^{63} +7.69606 q^{64} -5.04216 q^{65} +(1.71929 - 2.97791i) q^{66} +(-5.76482 + 9.98495i) q^{67} -2.10153 q^{68} -14.0823 q^{69} +(-0.863119 + 1.49497i) q^{70} +(3.11473 + 5.39488i) q^{71} +(-11.6267 + 20.1380i) q^{72} +(-6.05792 - 10.4926i) q^{73} +(-2.68365 - 4.64822i) q^{74} +10.7930 q^{75} +(-2.78776 + 2.68705i) q^{76} +1.25919 q^{77} +(6.66738 + 11.5482i) q^{78} +(-4.08003 - 7.06681i) q^{79} +(0.932501 - 1.61514i) q^{80} +(-13.1984 - 22.8602i) q^{81} +(-4.81966 + 8.34790i) q^{82} +4.25236 q^{83} -3.64775 q^{84} +(-1.53803 + 2.66395i) q^{85} +(0.207716 - 0.359774i) q^{86} +10.8144 q^{87} -3.04535 q^{88} +(-6.84735 + 11.8600i) q^{89} +(5.23392 + 9.06542i) q^{90} +(-2.44156 + 4.22890i) q^{91} +(1.91784 + 3.32180i) q^{92} +(13.6436 + 23.6314i) q^{93} -8.37089 q^{94} +(1.36592 + 5.50039i) q^{95} +14.9309 q^{96} +(-7.48677 - 12.9675i) q^{97} +(-2.85444 - 4.94403i) q^{98} +(3.81785 - 6.61271i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9}+O(q^{10}) $ 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9} + 21 q^{10} - 18 q^{11} + 16 q^{12} + 11 q^{13} + q^{14} + 7 q^{15} - 13 q^{16} + 6 q^{17} - 8 q^{18} + 4 q^{19} + 4 q^{20} + 24 q^{21} - q^{22} - q^{23} - 3 q^{24} - 7 q^{25} - 4 q^{26} + 6 q^{27} - 2 q^{28} + 13 q^{29} - 64 q^{30} - 32 q^{31} - 14 q^{32} + 8 q^{34} - 12 q^{35} + 10 q^{36} - 36 q^{37} - 20 q^{38} + 20 q^{39} + 32 q^{40} + 4 q^{41} + 11 q^{42} + q^{43} + 9 q^{44} + 22 q^{45} - 14 q^{46} - 14 q^{47} + 37 q^{48} - 12 q^{49} + 30 q^{50} - 16 q^{51} + 57 q^{52} - 4 q^{53} - 33 q^{54} - 34 q^{56} - 7 q^{57} + 8 q^{58} + 31 q^{59} + 9 q^{60} + 3 q^{61} + 5 q^{62} + 50 q^{63} + 64 q^{64} - 56 q^{65} + 3 q^{66} - 2 q^{67} - 96 q^{68} - 58 q^{70} - 12 q^{71} + 5 q^{72} - 26 q^{73} + 35 q^{74} + 50 q^{75} - 36 q^{76} + 6 q^{77} + 3 q^{78} + 31 q^{79} + 31 q^{80} - 21 q^{81} + 25 q^{82} + 36 q^{83} - 102 q^{84} - 11 q^{85} + 41 q^{86} - 124 q^{87} - 11 q^{89} + 51 q^{90} - 20 q^{91} - 33 q^{92} + 20 q^{93} - 86 q^{94} + 17 q^{95} + 60 q^{96} + 16 q^{97} + 4 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9 + 21 * q^10 - 18 * q^11 + 16 * q^12 + 11 * q^13 + q^14 + 7 * q^15 - 13 * q^16 + 6 * q^17 - 8 * q^18 + 4 * q^19 + 4 * q^20 + 24 * q^21 - q^22 - q^23 - 3 * q^24 - 7 * q^25 - 4 * q^26 + 6 * q^27 - 2 * q^28 + 13 * q^29 - 64 * q^30 - 32 * q^31 - 14 * q^32 + 8 * q^34 - 12 * q^35 + 10 * q^36 - 36 * q^37 - 20 * q^38 + 20 * q^39 + 32 * q^40 + 4 * q^41 + 11 * q^42 + q^43 + 9 * q^44 + 22 * q^45 - 14 * q^46 - 14 * q^47 + 37 * q^48 - 12 * q^49 + 30 * q^50 - 16 * q^51 + 57 * q^52 - 4 * q^53 - 33 * q^54 - 34 * q^56 - 7 * q^57 + 8 * q^58 + 31 * q^59 + 9 * q^60 + 3 * q^61 + 5 * q^62 + 50 * q^63 + 64 * q^64 - 56 * q^65 + 3 * q^66 - 2 * q^67 - 96 * q^68 - 58 * q^70 - 12 * q^71 + 5 * q^72 - 26 * q^73 + 35 * q^74 + 50 * q^75 - 36 * q^76 + 6 * q^77 + 3 * q^78 + 31 * q^79 + 31 * q^80 - 21 * q^81 + 25 * q^82 + 36 * q^83 - 102 * q^84 - 11 * q^85 + 41 * q^86 - 124 * q^87 - 11 * q^89 + 51 * q^90 - 20 * q^91 - 33 * q^92 + 20 * q^93 - 86 * q^94 + 17 * q^95 + 60 * q^96 + 16 * q^97 + 4 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.527190	+	0.913120i	0.372780	+	0.645674i	0.989992	−	0.141123i	$-0.0450713\pi$
$2$	0.527190	+	0.913120i	0.372780	+	0.645674i	−0.617212	+	0.786797i	$0.711738\pi$
$3$	1.63062	+	2.82432i	0.941439	+	1.63062i	0.762728	+	0.646719i	$0.223859\pi$
$3$	1.63062	+	2.82432i	0.941439	+	1.63062i	0.178711	+	0.983902i	$0.442807\pi$
$4$	0.444141	−	0.769275i	0.222070	−	0.384637i
$5$	−0.650102	−	1.12601i	−0.290734	−	0.503567i	0.683249	−	0.730185i	$-0.260566\pi$
$5$	−0.650102	−	1.12601i	−0.290734	−	0.503567i	−0.973984	+	0.226618i	$0.927233\pi$
$6$	−1.71929	+	2.97791i	−0.701899	+	1.21572i
$7$	−1.25919			−0.475930			−0.237965	−	0.971274i	$-0.576480\pi$
$7$	−1.25919			−0.475930			−0.237965	+	0.971274i	$0.576480\pi$
$8$	3.04535			1.07669
$9$	−3.81785	+	6.61271i	−1.27262	+	2.20424i
$10$	0.685455	−	1.18724i	0.216760	−	0.375439i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	2.89690			0.836263
$13$	1.93899	−	3.35842i	0.537778	−	0.931459i	−0.461245	−	0.887273i	$-0.652597\pi$
$13$	1.93899	−	3.35842i	0.537778	−	0.931459i	0.999023	−	0.0441865i	$-0.0140696\pi$
$14$	−0.663833	−	1.14979i	−0.177417	−	0.307295i
$15$	2.12014	−	3.67219i	0.547418	−	0.948155i
$16$	0.717196	+	1.24222i	0.179299	+	0.310555i
$17$	−1.18292	−	2.04887i	−0.286899	−	0.496924i	0.686169	−	0.727443i	$-0.259291\pi$
$17$	−1.18292	−	2.04887i	−0.286899	−	0.496924i	−0.973068	+	0.230518i	$0.925958\pi$
$18$	−8.05093			−1.89762
$19$	−4.18891	−	1.20541i	−0.961002	−	0.276540i
$19$	−4.18891	−	1.20541i	−0.961002	−	0.276540i
$20$	−1.15495			−0.258254
$21$	−2.05326	−	3.55636i	−0.448059	−	0.776061i
$22$	−0.527190	−	0.913120i	−0.112397	−	0.194678i
$23$	−2.15904	+	3.73957i	−0.450192	+	0.779755i	−0.998398	−	0.0565883i	$-0.981978\pi$
$23$	−2.15904	+	3.73957i	−0.450192	+	0.779755i	0.548206	+	0.836344i	$0.315311\pi$
$24$	4.96581	+	8.60103i	1.01364	+	1.75568i
$25$	1.65473	−	2.86608i	0.330947	−	0.573217i
$26$	4.08886			0.801892
$27$	−15.1181			−2.90948
$28$	−0.559258	+	0.968664i	−0.105690	+	0.183060i
$29$	1.65802	−	2.87177i	0.307887	−	0.533275i	−0.670013	−	0.742349i	$-0.733712\pi$
$29$	1.65802	−	2.87177i	0.307887	−	0.533275i	0.977900	+	0.209074i	$0.0670450\pi$
$30$	4.47087			0.816265
$31$	8.36713			1.50278			0.751390	−	0.659858i	$-0.229384\pi$
$31$	8.36713			1.50278			0.751390	+	0.659858i	$0.229384\pi$
$32$	2.28915	−	3.96492i	0.404668	−	0.700906i
$33$	−1.63062	−	2.82432i	−0.283855	−	0.491651i
$34$	1.24724	−	2.16029i	0.213901	−	0.370487i
$35$	0.818603	+	1.41786i	0.138369	+	0.239662i
$36$	3.39132	+	5.87395i	0.565221	+	0.978991i
$37$	−5.09048			−0.836869			−0.418435	−	0.908247i	$-0.637421\pi$
$37$	−5.09048			−0.836869			−0.418435	+	0.908247i	$0.637421\pi$
$38$	−1.10767	−	4.46046i	−0.179688	−	0.723582i
$39$	12.6470			2.02514
$40$	−1.97979	−	3.42909i	−0.313032	−	0.542187i
$41$	4.57108	+	7.91735i	0.713883	+	1.23648i	0.963389	+	0.268109i	$0.0863986\pi$
$41$	4.57108	+	7.91735i	0.713883	+	1.23648i	−0.249506	+	0.968373i	$0.580268\pi$
$42$	2.16492	−	3.74975i	0.334055	−	0.578599i
$43$	−0.197002	−	0.341218i	−0.0300426	−	0.0520353i	0.850613	−	0.525792i	$-0.176231\pi$
$43$	−0.197002	−	0.341218i	−0.0300426	−	0.0520353i	−0.880656	+	0.473757i	$0.842898\pi$
$44$	−0.444141	+	0.769275i	−0.0669568	+	0.115973i
$45$	9.92796			1.47997
$46$	−4.55291			−0.671290
$47$	−3.96958	+	6.87551i	−0.579022	+	1.00290i	0.416570	+	0.909104i	$0.363232\pi$
$47$	−3.96958	+	6.87551i	−0.579022	+	1.00290i	−0.995592	+	0.0937921i	$0.970101\pi$
$48$	−2.33895	+	4.05118i	−0.337598	+	0.584737i
$49$	−5.41444			−0.773491
$50$	3.48944			0.493481
$51$	3.85778	−	6.68187i	0.540197	−	0.935648i
$52$	−1.72237	−	2.98323i	−0.238849	−	0.413699i
$53$	1.53097	−	2.65172i	0.210295	−	0.364242i	−0.741512	−	0.670940i	$-0.765891\pi$
$53$	1.53097	−	2.65172i	0.210295	−	0.364242i	0.951807	+	0.306698i	$0.0992242\pi$
$54$	−7.97012	−	13.8047i	−1.08460	−	1.87858i
$55$	0.650102	+	1.12601i	0.0876597	+	0.151831i
$56$	−3.83468			−0.512430
$57$	−3.42607	−	13.7964i	−0.453794	−	1.82738i
$58$	3.49637			0.459095
$59$	2.47475	+	4.28639i	0.322185	+	0.558040i	0.980939	−	0.194318i	$-0.0622494\pi$
$59$	2.47475	+	4.28639i	0.322185	+	0.558040i	−0.658754	+	0.752359i	$0.728916\pi$
$60$	−1.88328	−	3.26194i	−0.243131	−	0.421114i
$61$	2.64087	−	4.57412i	0.338129	−	0.585656i	−0.645952	−	0.763378i	$-0.723539\pi$
$61$	2.64087	−	4.57412i	0.338129	−	0.585656i	0.984081	+	0.177722i	$0.0568727\pi$
$62$	4.41107	+	7.64020i	0.560206	+	0.970306i
$63$	4.80740	−	8.32666i	0.605676	−	1.04906i
$64$	7.69606			0.962007
$65$	−5.04216			−0.625403
$66$	1.71929	−	2.97791i	0.211631	−	0.366555i
$67$	−5.76482	+	9.98495i	−0.704284	+	1.21986i	0.262665	+	0.964887i	$0.415399\pi$
$67$	−5.76482	+	9.98495i	−0.704284	+	1.21986i	−0.966949	+	0.254969i	$0.917935\pi$
$68$	−2.10153			−0.254848
$69$	−14.0823			−1.69531
$70$	−0.863119	+	1.49497i	−0.103162	+	0.178683i
$71$	3.11473	+	5.39488i	0.369651	+	0.640254i	0.989511	−	0.144458i	$-0.0461440\pi$
$71$	3.11473	+	5.39488i	0.369651	+	0.640254i	−0.619860	+	0.784712i	$0.712811\pi$
$72$	−11.6267	+	20.1380i	−1.37022	+	2.37328i
$73$	−6.05792	−	10.4926i	−0.709026	−	1.22807i	−0.965219	−	0.261443i	$-0.915802\pi$
$73$	−6.05792	−	10.4926i	−0.709026	−	1.22807i	0.256193	−	0.966626i	$-0.417532\pi$
$74$	−2.68365	−	4.64822i	−0.311968	−	0.540344i
$75$	10.7930			1.24627
$76$	−2.78776	+	2.68705i	−0.319778	+	0.308226i
$77$	1.25919			0.143498
$78$	6.66738	+	11.5482i	0.754932	+	1.30758i
$79$	−4.08003	−	7.06681i	−0.459039	−	0.795078i	0.539872	−	0.841747i	$-0.318473\pi$
$79$	−4.08003	−	7.06681i	−0.459039	−	0.795078i	−0.998910	+	0.0466690i	$0.985139\pi$
$80$	0.932501	−	1.61514i	0.104257	−	0.180578i
$81$	−13.1984	−	22.8602i	−1.46649	−	2.54003i
$82$	−4.81966	+	8.34790i	−0.532242	+	0.921871i
$83$	4.25236			0.466757			0.233378	−	0.972386i	$-0.425022\pi$
$83$	4.25236			0.466757			0.233378	+	0.972386i	$0.425022\pi$
$84$	−3.64775			−0.398002
$85$	−1.53803	+	2.66395i	−0.166823	+	0.288946i
$86$	0.207716	−	0.359774i	0.0223985	−	0.0387954i
$87$	10.8144			1.15943
$88$	−3.04535			−0.324635
$89$	−6.84735	+	11.8600i	−0.725818	+	1.25715i	0.232818	+	0.972520i	$0.425205\pi$
$89$	−6.84735	+	11.8600i	−0.725818	+	1.25715i	−0.958636	+	0.284634i	$0.908128\pi$
$90$	5.23392	+	9.06542i	0.551704	+	0.955579i
$91$	−2.44156	+	4.22890i	−0.255945	+	0.443309i
$92$	1.91784	+	3.32180i	0.199949	+	0.346321i
$93$	13.6436	+	23.6314i	1.41478	+	2.45047i
$94$	−8.37089			−0.863391
$95$	1.36592	+	5.50039i	0.140140	+	0.564329i
$96$	14.9309			1.52388
$97$	−7.48677	−	12.9675i	−0.760167	−	1.31665i	−0.942764	−	0.333460i	$-0.891784\pi$
$97$	−7.48677	−	12.9675i	−0.760167	−	1.31665i	0.182598	−	0.983188i	$-0.441549\pi$
$98$	−2.85444	−	4.94403i	−0.288342	−	0.499423i
$99$	3.81785	−	6.61271i	0.383708	−	0.664602i
$100$	−1.46987	−	2.54589i	−0.146987	−	0.254589i
$101$	−0.509967	+	0.883289i	−0.0507437	+	0.0878906i	−0.890282	−	0.455411i	$-0.849492\pi$
$101$	−0.509967	+	0.883289i	−0.0507437	+	0.0878906i	0.839538	+	0.543301i	$0.182826\pi$
$102$	8.13513			0.805498
$103$	15.2045			1.49814			0.749070	−	0.662491i	$-0.230501\pi$
$103$	15.2045			1.49814			0.749070	+	0.662491i	$0.230501\pi$
$104$	5.90489	−	10.2276i	0.579022	−	1.00290i
$105$	−2.66966	+	4.62399i	−0.260532	+	0.451255i
$106$	3.22845			0.313575
$107$	−9.63111			−0.931074			−0.465537	−	0.885028i	$-0.654139\pi$
$107$	−9.63111			−0.931074			−0.465537	+	0.885028i	$0.654139\pi$
$108$	−6.71457	+	11.6300i	−0.646110	+	1.11910i
$109$	3.20158	+	5.54530i	0.306656	+	0.531143i	0.977629	−	0.210339i	$-0.0674566\pi$
$109$	3.20158	+	5.54530i	0.306656	+	0.531143i	−0.670973	+	0.741482i	$0.734123\pi$
$110$	−0.685455	+	1.18724i	−0.0653556	+	0.113199i
$111$	−8.30064	−	14.3771i	−0.787862	−	1.36462i
$112$	−0.903087	−	1.56419i	−0.0853337	−	0.147802i
$113$	3.43257			0.322909			0.161454	−	0.986880i	$-0.448382\pi$
$113$	3.43257			0.322909			0.161454	+	0.986880i	$0.448382\pi$
$114$	10.7916	−	10.4017i	1.01072	−	0.974212i
$115$	5.61440			0.523545
$116$	−1.47279	−	2.55094i	−0.136745	−	0.236849i
$117$	14.8055	+	25.6439i	1.36877	+	2.37078i
$118$	−2.60933	+	4.51949i	−0.240208	+	0.416052i
$119$	1.48952	+	2.57992i	0.136544	+	0.236501i
$120$	6.45656	−	11.1831i	0.589401	−	1.02087i
$121$	1.00000			0.0909091
$122$	5.56897			0.504190
$123$	−14.9074	+	25.8204i	−1.34416	+	2.32815i
$124$	3.71618	−	6.43662i	0.333723	−	0.578025i
$125$	−10.8040			−0.966340
$126$	10.1377			0.903134
$127$	−9.22346	+	15.9755i	−0.818450	+	1.41760i	0.0883748	+	0.996087i	$0.471833\pi$
$127$	−9.22346	+	15.9755i	−0.818450	+	1.41760i	−0.906824	+	0.421509i	$0.861501\pi$
$128$	−0.521015	−	0.902425i	−0.0460517	−	0.0797639i
$129$	0.642473	−	1.11280i	0.0565666	−	0.0979761i
$130$	−2.65818	−	4.60410i	−0.233137	−	0.403806i
$131$	−6.80426	−	11.7853i	−0.594491	−	1.02969i	−0.993619	−	0.112793i	$-0.964020\pi$
$131$	−6.80426	−	11.7853i	−0.594491	−	1.02969i	0.399128	−	0.916895i	$-0.369313\pi$
$132$	−2.89690			−0.252143
$133$	5.27464	+	1.51784i	0.457370	+	0.131613i
$134$	−12.1566			−1.05017
$135$	9.82832	+	17.0231i	0.845887	+	1.46512i
$136$	−3.60239	−	6.23953i	−0.308903	−	0.535035i
$137$	−5.69088	+	9.85689i	−0.486205	+	0.842131i	−0.999874	−	0.0158570i	$-0.994952\pi$
$137$	−5.69088	+	9.85689i	−0.486205	+	0.842131i	0.513670	+	0.857988i	$0.328286\pi$
$138$	−7.42407	−	12.8589i	−0.631979	−	1.09462i
$139$	3.35997	−	5.81963i	0.284989	−	0.493615i	−0.687618	−	0.726073i	$-0.741343\pi$
$139$	3.35997	−	5.81963i	0.284989	−	0.493615i	0.972606	+	0.232458i	$0.0746768\pi$
$140$	1.45430			0.122911
$141$	−25.8915			−2.18046
$142$	−3.28411	+	5.68825i	−0.275597	+	0.477347i
$143$	−1.93899	+	3.35842i	−0.162146	+	0.280846i
$144$	−10.9526			−0.912715
$145$	−4.31153			−0.358053
$146$	6.38735	−	11.0632i	0.528621	−	0.915599i
$147$	−8.82889	−	15.2921i	−0.728195	−	1.26127i
$148$	−2.26089	+	3.91597i	−0.185844	+	0.321891i
$149$	11.8328	+	20.4950i	0.969379	+	1.67901i	0.697359	+	0.716722i	$0.254358\pi$
$149$	11.8328	+	20.4950i	0.969379	+	1.67901i	0.272020	+	0.962292i	$0.412308\pi$
$150$	5.68995	+	9.85529i	0.464583	+	0.804681i
$151$	−18.1209			−1.47466			−0.737329	−	0.675534i	$-0.763913\pi$
$151$	−18.1209			−1.47466			−0.737329	+	0.675534i	$0.763913\pi$
$152$	−12.7567	−	3.67089i	−1.03470	−	0.297748i
$153$	18.0648			1.46045
$154$	0.663833	+	1.14979i	0.0534932	+	0.0926530i
$155$	−5.43949	−	9.42147i	−0.436910	−	0.756751i
$156$	5.61705	−	9.72902i	0.449724	−	0.778945i
$157$	3.07311	+	5.32278i	0.245261	+	0.424804i	0.962205	−	0.272327i	$-0.0877931\pi$
$157$	3.07311	+	5.32278i	0.245261	+	0.424804i	−0.716944	+	0.697131i	$0.754460\pi$
$158$	4.30190	−	7.45111i	0.342241	−	0.592778i
$159$	9.98573			0.791920
$160$	−5.95272			−0.470604
$161$	2.71865	−	4.70884i	0.214260	−	0.371109i
$162$	13.9161	−	24.1034i	1.09335	−	1.89374i
$163$	−1.66474			−0.130392			−0.0651961	−	0.997872i	$-0.520767\pi$
$163$	−1.66474			−0.130392			−0.0651961	+	0.997872i	$0.520767\pi$
$164$	8.12082			0.634129
$165$	−2.12014	+	3.67219i	−0.165053	+	0.285880i
$166$	2.24180	+	3.88291i	0.173997	+	0.301372i
$167$	9.24297	−	16.0093i	0.715243	−	1.23884i	−0.247623	−	0.968856i	$-0.579649\pi$
$167$	9.24297	−	16.0093i	0.715243	−	1.23884i	0.962866	−	0.269980i	$-0.0870172\pi$
$168$	−6.25290	−	10.8303i	−0.482422	−	0.835579i
$169$	−1.01934	−	1.76555i	−0.0784110	−	0.135812i
$170$	−3.24334			−0.248753
$171$	23.9636	−	23.0980i	1.83255	−	1.76635i
$172$	−0.349987			−0.0266863
$173$	−2.56782	−	4.44759i	−0.195227	−	0.338144i	0.751748	−	0.659451i	$-0.229211\pi$
$173$	−2.56782	−	4.44759i	−0.195227	−	0.338144i	−0.946975	+	0.321307i	$0.895878\pi$
$174$	5.70125	+	9.87485i	0.432211	+	0.748611i
$175$	−2.08363	+	3.60895i	−0.157507	+	0.272811i
$176$	−0.717196	−	1.24222i	−0.0540607	−	0.0936359i
$177$	−8.07075	+	13.9790i	−0.606635	+	1.05072i
$178$	−14.4394			−1.08228
$179$	14.4948			1.08339			0.541696	−	0.840574i	$-0.317782\pi$
$179$	14.4948			1.08339			0.541696	+	0.840574i	$0.317782\pi$
$180$	4.40941	−	7.63733i	0.328658	−	0.569253i
$181$	3.30476	−	5.72401i	0.245641	−	0.425462i	−0.716671	−	0.697411i	$-0.754335\pi$
$181$	3.30476	−	5.72401i	0.245641	−	0.425462i	0.962312	+	0.271950i	$0.0876684\pi$
$182$	−5.14866			−0.381644
$183$	17.2250			1.27331
$184$	−6.57504	+	11.3883i	−0.484719	+	0.839557i
$185$	3.30933	+	5.73193i	0.243307	+	0.421420i
$186$	−14.3856	+	24.9165i	−1.05480	+	1.82697i
$187$	1.18292	+	2.04887i	0.0865034	+	0.149828i
$188$	3.52610	+	6.10739i	0.257167	+	0.445427i
$189$	19.0366			1.38471
$190$	−4.30242	+	4.14700i	−0.312131	+	0.300855i
$191$	4.93176			0.356850			0.178425	−	0.983954i	$-0.442900\pi$
$191$	4.93176			0.356850			0.178425	+	0.983954i	$0.442900\pi$
$192$	12.5493	+	21.7361i	0.905671	+	1.56867i
$193$	−2.71484	−	4.70224i	−0.195419	−	0.338475i	0.751619	−	0.659597i	$-0.229273\pi$
$193$	−2.71484	−	4.70224i	−0.195419	−	0.338475i	−0.947038	+	0.321122i	$0.895940\pi$
$194$	7.89391	−	13.6727i	0.566750	−	0.981639i
$195$	−8.22185	−	14.2407i	−0.588779	−	1.01979i
$196$	−2.40477	+	4.16519i	−0.171769	+	0.297513i
$197$	3.83112			0.272956			0.136478	−	0.990643i	$-0.456422\pi$
$197$	3.83112			0.272956			0.136478	+	0.990643i	$0.456422\pi$
$198$	8.05093			0.572154
$199$	8.96772	−	15.5325i	0.635705	−	1.10107i	−0.350661	−	0.936503i	$-0.614043\pi$
$199$	8.96772	−	15.5325i	0.635705	−	1.10107i	0.986365	−	0.164570i	$-0.0526237\pi$
$200$	5.03924	−	8.72823i	0.356328	−	0.617179i
$201$	−37.6009			−2.65216
$202$	−1.07540			−0.0756648
$203$	−2.08776	+	3.61611i	−0.146532	+	0.253801i
$204$	−3.42679	−	5.93538i	−0.239923	−	0.415560i
$205$	5.94334	−	10.2942i	0.415101	−	0.718976i
$206$	8.01565	+	13.8835i	0.558477	+	0.967310i
$207$	−16.4858	−	28.5542i	−1.14584	−	1.98466i
$208$	5.56254			0.385692
$209$	4.18891	+	1.20541i	0.289753	+	0.0833799i
$210$	−5.62968			−0.388485
$211$	1.46757	+	2.54190i	0.101031	+	0.174992i	0.912110	−	0.409946i	$-0.134452\pi$
$211$	1.46757	+	2.54190i	0.101031	+	0.174992i	−0.811078	+	0.584937i	$0.801119\pi$
$212$	−1.35993	−	2.35547i	−0.0934007	−	0.161775i
$213$	−10.1579	+	17.5940i	−0.696008	+	1.20552i
$214$	−5.07743	−	8.79436i	−0.347086	−	0.601170i
$215$	−0.256143	+	0.443653i	−0.0174688	+	0.0302569i
$216$	−46.0399			−3.13262
$217$	−10.5358			−0.715218
$218$	−3.37568	+	5.84685i	−0.228630	+	0.395999i
$219$	19.7563	−	34.2190i	1.33501	−	2.31230i
$220$	1.15495			0.0778665
$221$	−9.17464			−0.617153
$222$	8.75203	−	15.1590i	0.587398	−	1.01740i
$223$	3.62730	+	6.28266i	0.242902	+	0.420718i	0.961540	−	0.274666i	$-0.0885674\pi$
$223$	3.62730	+	6.28266i	0.242902	+	0.420718i	−0.718638	+	0.695385i	$0.755234\pi$
$224$	−2.88248	+	4.99260i	−0.192594	+	0.333582i
$225$	12.6350	+	21.8845i	0.842337	+	1.45897i
$226$	1.80962	+	3.13435i	0.120374	+	0.208494i
$227$	15.3941			1.02175			0.510873	−	0.859656i	$-0.329322\pi$
$227$	15.3941			1.02175			0.510873	+	0.859656i	$0.329322\pi$
$228$	−12.1349	−	3.49195i	−0.803651	−	0.231260i
$229$	5.28204			0.349047			0.174524	−	0.984653i	$-0.444161\pi$
$229$	5.28204			0.349047			0.174524	+	0.984653i	$0.444161\pi$
$230$	2.95986	+	5.12662i	0.195167	+	0.338039i
$231$	2.05326	+	3.55636i	0.135095	+	0.233991i
$232$	5.04925	−	8.74555i	0.331499	−	0.574174i
$233$	10.3416	+	17.9123i	0.677504	+	1.17347i	0.975730	+	0.218976i	$0.0702717\pi$
$233$	10.3416	+	17.9123i	0.677504	+	1.17347i	−0.298226	+	0.954495i	$0.596395\pi$
$234$	−15.6106	+	27.0384i	−1.02050	+	1.76756i
$235$	10.3225			0.673367
$236$	4.39655			0.286191
$237$	13.3059	−	23.0466i	0.864314	−	1.49704i
$238$	−1.57052	+	2.72022i	−0.101802	+	0.176326i
$239$	−17.7320			−1.14699			−0.573494	−	0.819210i	$-0.694412\pi$
$239$	−17.7320			−1.14699			−0.573494	+	0.819210i	$0.694412\pi$
$240$	6.08222			0.392606
$241$	6.99801	−	12.1209i	0.450782	−	0.780777i	−0.547653	−	0.836705i	$-0.684479\pi$
$241$	6.99801	−	12.1209i	0.450782	−	0.780777i	0.998435	+	0.0559289i	$0.0178120\pi$
$242$	0.527190	+	0.913120i	0.0338891	+	0.0586976i
$243$	20.3659	−	35.2748i	1.30647	−	2.26288i
$244$	−2.34584	−	4.06311i	−0.150177	−	0.260114i
$245$	3.51994	+	6.09671i	0.224880	+	0.389504i
$246$	−31.4362			−2.00430
$247$	−12.1705	+	11.7309i	−0.774392	+	0.746418i
$248$	25.4808			1.61803
$249$	6.93398	+	12.0100i	0.439423	+	0.761103i
$250$	−5.69577	−	9.86536i	−0.360232	−	0.623940i
$251$	5.87445	−	10.1748i	0.370792	−	0.642230i	−0.618896	−	0.785473i	$-0.712420\pi$
$251$	5.87445	−	10.1748i	0.370792	−	0.642230i	0.989688	+	0.143243i	$0.0457530\pi$
$252$	−4.27033	−	7.39642i	−0.269005	−	0.465931i
$253$	2.15904	−	3.73957i	0.135738	−	0.235105i
$254$	−19.4501			−1.22041
$255$	−10.0318			−0.628215
$256$	8.24540	−	14.2815i	0.515338	−	0.892591i
$257$	11.7995	−	20.4373i	0.736033	−	1.27485i	−0.218236	−	0.975896i	$-0.570030\pi$
$257$	11.7995	−	20.4373i	0.736033	−	1.27485i	0.954269	−	0.298950i	$-0.0966365\pi$
$258$	1.35482			0.0843475
$259$	6.40988			0.398291
$260$	−2.23943	+	3.87880i	−0.138883	+	0.240553i
$261$	12.6601	+	21.9280i	0.783642	+	1.35731i
$262$	7.17428	−	12.4262i	0.443228	−	0.767694i
$263$	−0.130693	−	0.226367i	−0.00805888	−	0.0139584i	0.861968	−	0.506963i	$-0.169232\pi$
$263$	−0.130693	−	0.226367i	−0.00805888	−	0.0139584i	−0.870027	+	0.493005i	$0.835899\pi$
$264$	−4.96581	−	8.60103i	−0.305624	−	0.529357i
$265$	−3.98115			−0.244560
$266$	1.39477	+	5.61657i	0.0855188	+	0.344374i
$267$	−44.6617			−2.73325
$268$	5.12078	+	8.86945i	0.312801	+	0.541788i
$269$	−5.88167	−	10.1874i	−0.358612	−	0.621134i	0.629117	−	0.777310i	$-0.283417\pi$
$269$	−5.88167	−	10.1874i	−0.358612	−	0.621134i	−0.987729	+	0.156176i	$0.950083\pi$
$270$	−10.3628	+	17.9489i	−0.630659	+	1.09233i
$271$	13.3047	+	23.0445i	0.808206	+	1.39985i	0.914106	+	0.405476i	$0.132894\pi$
$271$	13.3047	+	23.0445i	0.808206	+	1.39985i	−0.105900	+	0.994377i	$0.533772\pi$
$272$	1.69677	−	2.93889i	0.102882	−	0.178196i
$273$	−15.9250			−0.963825
$274$	−12.0007			−0.724989
$275$	−1.65473	+	2.86608i	−0.0997843	+	0.172831i
$276$	−6.25454	+	10.8332i	−0.376479	+	0.652081i
$277$	11.6928			0.702551			0.351275	−	0.936272i	$-0.385748\pi$
$277$	11.6928			0.702551			0.351275	+	0.936272i	$0.385748\pi$
$278$	7.08537			0.424952
$279$	−31.9444	+	55.3294i	−1.91246	+	3.31248i
$280$	2.49293	+	4.31788i	0.148981	+	0.258043i
$281$	−10.6765	+	18.4923i	−0.636908	+	1.10316i	0.349200	+	0.937048i	$0.386453\pi$
$281$	−10.6765	+	18.4923i	−0.636908	+	1.10316i	−0.986108	+	0.166108i	$0.946880\pi$
$282$	−13.6497	−	23.6420i	−0.812830	−	1.40786i
$283$	6.29592	+	10.9048i	0.374253	+	0.648226i	0.990215	−	0.139550i	$-0.0445657\pi$
$283$	6.29592	+	10.9048i	0.374253	+	0.648226i	−0.615962	+	0.787776i	$0.711232\pi$
$284$	5.53352			0.328354
$285$	−13.3076	+	12.8268i	−0.788272	+	0.759797i
$286$	−4.08886			−0.241779
$287$	−5.75587	−	9.96946i	−0.339758	−	0.588478i
$288$	17.4793	+	30.2750i	1.02997	+	1.78397i
$289$	5.70142	−	9.87514i	0.335377	−	0.580891i
$290$	−2.27300	−	3.93694i	−0.133475	−	0.231185i
$291$	24.4162	−	42.2901i	1.43130	−	2.47909i
$292$	−10.7623			−0.629815
$293$	−13.2537			−0.774289			−0.387145	−	0.922019i	$-0.626539\pi$
$293$	−13.2537			−0.774289			−0.387145	+	0.922019i	$0.626539\pi$
$294$	9.30901	−	16.1237i	0.542913	−	0.940352i
$295$	3.21768	−	5.57318i	0.187340	−	0.324483i
$296$	−15.5023			−0.901051
$297$	15.1181			0.877242
$298$	−12.4763	+	21.6095i	−0.722730	+	1.25180i
$299$	8.37272	+	14.5020i	0.484207	+	0.838671i
$300$	4.79360	−	8.30276i	0.276759	−	0.479360i
$301$	0.248064	+	0.429659i	0.0142982	+	0.0247651i
$302$	−9.55316	−	16.5466i	−0.549722	−	0.952147i
$303$	−3.32625			−0.191088
$304$	−1.50689	−	6.06807i	−0.0864260	−	0.348027i
$305$	−6.86734			−0.393223
$306$	9.52358	+	16.4953i	0.544427	+	0.942975i
$307$	−0.616227	−	1.06734i	−0.0351699	−	0.0609161i	0.847905	−	0.530149i	$-0.177864\pi$
$307$	−0.616227	−	1.06734i	−0.0351699	−	0.0609161i	−0.883075	+	0.469233i	$0.844531\pi$
$308$	0.559258	−	0.968664i	0.0318667	−	0.0551947i
$309$	24.7927	+	42.9422i	1.41041	+	2.44290i
$310$	5.73529	−	9.93381i	0.325743	−	0.564203i
$311$	17.4587			0.989994			0.494997	−	0.868895i	$-0.335169\pi$
$311$	17.4587			0.989994			0.494997	+	0.868895i	$0.335169\pi$
$312$	38.5145			2.18046
$313$	−13.5568	+	23.4811i	−0.766276	+	1.32723i	0.173293	+	0.984870i	$0.444559\pi$
$313$	−13.5568	+	23.4811i	−0.766276	+	1.32723i	−0.939569	+	0.342359i	$0.888774\pi$
$314$	−3.24023	+	5.61224i	−0.182857	+	0.316717i
$315$	−12.5012			−0.704363
$316$	−7.24842			−0.407756
$317$	6.18283	−	10.7090i	0.347262	−	0.601476i	−0.638500	−	0.769622i	$-0.720445\pi$
$317$	6.18283	−	10.7090i	0.347262	−	0.601476i	0.985762	+	0.168146i	$0.0537780\pi$
$318$	5.26438	+	9.11818i	0.295212	+	0.511322i
$319$	−1.65802	+	2.87177i	−0.0928313	+	0.160788i
$320$	−5.00322	−	8.66583i	−0.279689	−	0.484435i
$321$	−15.7047	−	27.2013i	−0.876550	−	1.51823i
$322$	5.73298			0.319487
$323$	2.48541	+	10.0084i	0.138292	+	0.556885i
$324$	−23.4477			−1.30265
$325$	−6.41702	−	11.1146i	−0.355952	−	0.616527i
$326$	−0.877632	−	1.52010i	−0.0486076	−	0.0841908i
$327$	−10.4411	+	18.0846i	−0.577395	+	1.00008i
$328$	13.9205	+	24.1111i	0.768633	+	1.33131i
$329$	4.99846	−	8.65758i	0.275574	−	0.477308i
$330$	−4.47087			−0.246113
$331$	34.6565			1.90489			0.952446	−	0.304706i	$-0.0985583\pi$
$331$	34.6565			1.90489			0.952446	+	0.304706i	$0.0985583\pi$
$332$	1.88865	−	3.27123i	0.103653	−	0.179532i
$333$	19.4347	−	33.6618i	1.06501	−	1.84466i
$334$	19.4912			1.06651
$335$	14.9909			0.819039
$336$	2.94518	−	5.10121i	0.160673	−	0.278294i
$337$	5.64069	+	9.76996i	0.307268	+	0.532204i	0.977764	−	0.209710i	$-0.0672519\pi$
$337$	5.64069	+	9.76996i	0.307268	+	0.532204i	−0.670496	+	0.741913i	$0.733919\pi$
$338$	1.07477	−	1.86156i	0.0584600	−	0.101256i
$339$	5.59722	+	9.69466i	0.303999	+	0.526542i
$340$	1.36621	+	2.36634i	0.0740930	+	0.128333i
$341$	−8.36713			−0.453105
$342$	33.7246	+	9.70466i	1.82362	+	0.524768i
$343$	15.6322			0.844057
$344$	−0.599941	−	1.03913i	−0.0323467	−	0.0560260i
$345$	9.15495	+	15.8568i	0.492886	+	0.853704i
$346$	2.70745	−	4.68945i	0.145554	−	0.252106i
$347$	−3.63792	−	6.30105i	−0.195294	−	0.338258i	0.751703	−	0.659502i	$-0.229233\pi$
$347$	−3.63792	−	6.30105i	−0.195294	−	0.338258i	−0.946997	+	0.321243i	$0.895899\pi$
$348$	4.80312	−	8.31925i	0.257474	−	0.445958i
$349$	24.2963			1.30055			0.650276	−	0.759698i	$-0.274653\pi$
$349$	24.2963			1.30055			0.650276	+	0.759698i	$0.274653\pi$
$350$	−4.39387			−0.234862
$351$	−29.3138	+	50.7730i	−1.56466	+	2.71006i
$352$	−2.28915	+	3.96492i	−0.122012	+	0.211331i
$353$	−28.9238			−1.53946			−0.769730	−	0.638369i	$-0.779609\pi$
$353$	−28.9238			−1.53946			−0.769730	+	0.638369i	$0.779609\pi$
$354$	−17.0193			−0.904565
$355$	4.04979	−	7.01444i	0.214940	−	0.372288i
$356$	6.08238	+	10.5350i	0.322365	+	0.558353i
$357$	−4.85768	+	8.41375i	−0.257096	+	0.445303i
$358$	7.64152	+	13.2355i	0.403867	+	0.699518i
$359$	−9.54571	−	16.5337i	−0.503803	−	0.872613i	−0.999990	−	0.00439720i	$-0.998600\pi$
$359$	−9.54571	−	16.5337i	−0.503803	−	0.872613i	0.496187	−	0.868216i	$-0.334733\pi$
$360$	30.2341			1.59348
$361$	16.0940	+	10.0987i	0.847052	+	0.531511i
$362$	6.96894			0.366279
$363$	1.63062	+	2.82432i	0.0855854	+	0.148238i
$364$	2.16879	+	3.75645i	0.113675	+	0.196892i
$365$	−7.87653	+	13.6426i	−0.412277	+	0.714084i
$366$	9.08087	+	15.7285i	0.474665	+	0.822143i
$367$	11.1118	−	19.2463i	0.580034	−	1.00465i	−0.415441	−	0.909620i	$-0.636373\pi$
$367$	11.1118	−	19.2463i	0.580034	−	1.00465i	0.995475	−	0.0950278i	$-0.0302940\pi$
$368$	−6.19383			−0.322876
$369$	−69.8068			−3.63400
$370$	−3.48929	+	6.04363i	−0.181400	+	0.314193i
$371$	−1.92779	+	3.33902i	−0.100086	+	0.173353i
$372$	24.2387			1.25672
$373$	−20.3431			−1.05333			−0.526664	−	0.850074i	$-0.676557\pi$
$373$	−20.3431			−1.05333			−0.526664	+	0.850074i	$0.676557\pi$
$374$	−1.24724	+	2.16029i	−0.0644935	+	0.111706i
$375$	−17.6172	−	30.5139i	−0.909750	−	1.57573i
$376$	−12.0887	+	20.9383i	−0.623429	+	1.07981i
$377$	−6.42976	−	11.1367i	−0.331149	−	0.573568i
$378$	10.0359	+	17.3827i	0.516192	+	0.894070i
$379$	17.4613			0.896924			0.448462	−	0.893802i	$-0.351972\pi$
$379$	17.4613			0.896924			0.448462	+	0.893802i	$0.351972\pi$
$380$	4.83797	+	1.39218i	0.248183	+	0.0714175i
$381$	−60.1598			−3.08208
$382$	2.59998	+	4.50329i	0.133026	+	0.230408i
$383$	1.23348	+	2.13645i	0.0630280	+	0.109168i	0.895818	−	0.444422i	$-0.146591\pi$
$383$	1.23348	+	2.13645i	0.0630280	+	0.109168i	−0.832790	+	0.553590i	$0.813258\pi$
$384$	1.69916	−	2.94303i	0.0867098	−	0.150186i
$385$	−0.818603	−	1.41786i	−0.0417199	−	0.0722609i
$386$	2.86248	−	4.95796i	0.145696	−	0.252353i
$387$	3.00850			0.152931
$388$	−13.3007			−0.675242
$389$	6.65147	−	11.5207i	0.337243	−	0.584122i	−0.646670	−	0.762770i	$-0.723839\pi$
$389$	6.65147	−	11.5207i	0.337243	−	0.584122i	0.983913	+	0.178648i	$0.0571723\pi$
$390$	8.66895	−	15.0151i	0.438970	−	0.760318i
$391$	10.2159			0.516639
$392$	−16.4888			−0.832812
$393$	22.1903	−	38.4348i	1.11935	−	1.93878i
$394$	2.01973	+	3.49828i	0.101753	+	0.176241i
$395$	−5.30486	+	9.18830i	−0.266917	+	0.462313i
$396$	−3.39132	−	5.87395i	−0.170420	−	0.295177i
$397$	3.37900	+	5.85261i	0.169587	+	0.293734i	0.938275	−	0.345891i	$-0.112423\pi$
$397$	3.37900	+	5.85261i	0.169587	+	0.293734i	−0.768688	+	0.639625i	$0.779090\pi$
$398$	18.9108			0.947911
$399$	4.31408	+	17.3723i	0.215974	+	0.869702i
$400$	4.74708			0.237354
$401$	−9.73894	−	16.8683i	−0.486339	−	0.842365i	0.513537	−	0.858067i	$-0.328335\pi$
$401$	−9.73894	−	16.8683i	−0.486339	−	0.842365i	−0.999877	+	0.0157026i	$0.995002\pi$
$402$	−19.8228	−	34.3342i	−0.988673	−	1.71243i
$403$	16.2238	−	28.1004i	0.808163	−	1.39978i
$404$	0.452995	+	0.784610i	0.0225373	+	0.0390358i
$405$	−17.1606	+	29.7230i	−0.852716	+	1.47695i
$406$	−4.40260			−0.218497
$407$	5.09048			0.252326
$408$	11.7483	−	20.3486i	0.581626	−	1.00741i
$409$	−2.23866	+	3.87748i	−0.110695	+	0.191729i	−0.916051	−	0.401063i	$-0.868641\pi$
$409$	−2.23866	+	3.87748i	−0.110695	+	0.191729i	0.805356	+	0.592792i	$0.201974\pi$
$410$	12.5331			0.618965
$411$	−37.1187			−1.83093
$412$	6.75292	−	11.6964i	0.332693	−	0.576241i
$413$	−3.11618	−	5.39739i	−0.153337	−	0.265588i
$414$	17.3823	−	30.1070i	0.854294	−	1.47968i
$415$	−2.76447	−	4.78819i	−0.135702	−	0.235043i
$416$	−8.87727	−	15.3759i	−0.435244	−	0.753864i
$417$	21.9153			1.07320
$418$	1.10767	+	4.46046i	0.0541779	+	0.218168i
$419$	−27.2745			−1.33245			−0.666223	−	0.745753i	$-0.732090\pi$
$419$	−27.2745			−1.33245			−0.666223	+	0.745753i	$0.732090\pi$
$420$	2.37141	+	4.10740i	0.115713	+	0.200421i
$421$	−13.0453	−	22.5952i	−0.635791	−	1.10122i	−0.986347	−	0.164681i	$-0.947341\pi$
$421$	−13.0453	−	22.5952i	−0.635791	−	1.10122i	0.350555	−	0.936542i	$-0.385993\pi$
$422$	−1.54737	+	2.68013i	−0.0753249	+	0.130467i
$423$	−30.3105	−	52.4993i	−1.47375	−	2.55260i
$424$	4.66234	−	8.07541i	0.226423	−	0.392177i
$425$	−7.82965			−0.379794
$426$	−21.4206			−1.03783
$427$	−3.32536	+	5.75970i	−0.160926	+	0.278731i
$428$	−4.27757	+	7.40897i	−0.206764	+	0.358126i
$429$	−12.6470			−0.610603
$430$	−0.540145			−0.0260481
$431$	−16.8860	+	29.2474i	−0.813369	+	1.40880i	0.0971243	+	0.995272i	$0.469036\pi$
$431$	−16.8860	+	29.2474i	−0.813369	+	1.40880i	−0.910493	+	0.413524i	$0.864298\pi$
$432$	−10.8427	−	18.7800i	−0.521667	−	0.903554i
$433$	3.30632	−	5.72671i	0.158892	−	0.275208i	−0.775578	−	0.631252i	$-0.782541\pi$
$433$	3.30632	−	5.72671i	0.158892	−	0.275208i	0.934469	+	0.356044i	$0.115875\pi$
$434$	−5.55438	−	9.62047i	−0.266619	−	0.461797i
$435$	−7.03047	−	12.1771i	−0.337085	−	0.583848i
$436$	5.68781			0.272397
$437$	13.5518	−	13.0622i	0.648269	−	0.624851i
$438$	41.6614			1.99066
$439$	2.07719	+	3.59779i	0.0991387	+	0.171713i	0.911328	−	0.411680i	$-0.135058\pi$
$439$	2.07719	+	3.59779i	0.0991387	+	0.171713i	−0.812190	+	0.583393i	$0.801725\pi$
$440$	1.97979	+	3.42909i	0.0943826	+	0.163476i
$441$	20.6715	−	35.8041i	0.984357	−	1.70496i
$442$	−4.83678	−	8.37755i	−0.230062	−	0.398480i
$443$	−6.35220	+	11.0023i	−0.301802	+	0.522737i	−0.976544	−	0.215317i	$-0.930922\pi$
$443$	−6.35220	+	11.0023i	−0.301802	+	0.522737i	0.674742	+	0.738054i	$0.264255\pi$
$444$	−14.7466			−0.699843
$445$	17.8059			0.844081
$446$	−3.82455	+	6.62432i	−0.181098	+	0.313670i
$447$	−38.5895	+	66.8391i	−1.82522	+	3.16138i
$448$	−9.69081			−0.457848
$449$	−16.3134			−0.769877			−0.384939	−	0.922942i	$-0.625777\pi$
$449$	−16.3134			−0.769877			−0.384939	+	0.922942i	$0.625777\pi$
$450$	−13.3221	+	23.0746i	−0.628012	+	1.08775i
$451$	−4.57108	−	7.91735i	−0.215244	−	0.372813i
$452$	1.52454	−	2.64059i	0.0717085	−	0.124203i
$453$	−29.5483	−	51.1792i	−1.38830	−	2.40461i
$454$	8.11565	+	14.0567i	0.380886	+	0.659714i
$455$	6.34904			0.297648
$456$	−10.4336	−	42.0148i	−0.488597	−	1.96752i
$457$	1.12550			0.0526487			0.0263244	−	0.999653i	$-0.491620\pi$
$457$	1.12550			0.0526487			0.0263244	+	0.999653i	$0.491620\pi$
$458$	2.78464	+	4.82314i	0.130118	+	0.225371i
$459$	17.8835	+	30.9751i	0.834729	+	1.44579i
$460$	2.49358	−	4.31901i	0.116264	−	0.201375i
$461$	3.72459	+	6.45117i	0.173471	+	0.300461i	0.939631	−	0.342189i	$-0.111168\pi$
$461$	3.72459	+	6.45117i	0.173471	+	0.300461i	−0.766160	+	0.642650i	$0.777835\pi$
$462$	−2.16492	+	3.74975i	−0.100721	+	0.174454i
$463$	0.578694			0.0268942			0.0134471	−	0.999910i	$-0.495720\pi$
$463$	0.578694			0.0268942			0.0134471	+	0.999910i	$0.495720\pi$
$464$	4.75650			0.220815
$465$	17.7395	−	30.7257i	0.822649	−	1.42487i
$466$	−10.9040	+	18.8863i	−0.505120	+	0.874893i
$467$	−20.0171			−0.926280			−0.463140	−	0.886285i	$-0.653277\pi$
$467$	−20.0171			−0.926280			−0.463140	+	0.886285i	$0.653277\pi$
$468$	26.3029			1.21585
$469$	7.25901	−	12.5730i	0.335190	−	0.580566i
$470$	5.44193	+	9.42570i	0.251018	+	0.434775i
$471$	−10.0221	+	17.3589i	−0.461796	+	0.799854i
$472$	7.53647	+	13.0536i	0.346894	+	0.600838i
$473$	0.197002	+	0.341218i	0.00905818	+	0.0156892i
$474$	28.0591			1.28880
$475$	−10.3863	+	10.0111i	−0.476558	+	0.459343i
$476$	2.64622			0.121290
$477$	11.6900	+	20.2477i	0.535250	+	0.927080i
$478$	−9.34814	−	16.1914i	−0.427574	−	0.740580i
$479$	8.88502	−	15.3893i	0.405967	−	0.703155i	−0.588466	−	0.808522i	$-0.700268\pi$
$479$	8.88502	−	15.3893i	0.405967	−	0.703155i	0.994433	+	0.105366i	$0.0336014\pi$
$480$	−9.70664	−	16.8124i	−0.443045	−	0.767377i
$481$	−9.87037	+	17.0960i	−0.450050	+	0.779510i
$482$	14.7571			0.672169
$483$	17.7323			0.806850
$484$	0.444141	−	0.769275i	0.0201882	−	0.0349670i
$485$	−9.73433	+	16.8604i	−0.442013	+	0.765589i
$486$	42.9468			1.94811
$487$	2.82029			0.127799			0.0638997	−	0.997956i	$-0.479646\pi$
$487$	2.82029			0.127799			0.0638997	+	0.997956i	$0.479646\pi$
$488$	8.04237	−	13.9298i	0.364061	−	0.630572i
$489$	−2.71455	−	4.70174i	−0.122756	−	0.212620i
$490$	−3.71135	+	6.42825i	−0.167662	+	0.290399i
$491$	0.0102158	+	0.0176943i	0.000461033	+	0.000798532i	0.866256	−	0.499601i	$-0.166520\pi$
$491$	0.0102158	+	0.0176943i	0.000461033	+	0.000798532i	−0.865795	+	0.500399i	$0.833187\pi$
$492$	13.2420	+	22.9358i	0.596994	+	1.03402i
$493$	−7.84520			−0.353330
$494$	−17.1279	−	4.92875i	−0.770620	−	0.221755i
$495$	−9.92796			−0.446229
$496$	6.00087	+	10.3938i	0.269447	+	0.466696i
$497$	−3.92205	−	6.79318i	−0.175928	−	0.304716i
$498$	−7.31105	+	12.6631i	−0.327616	+	0.567448i
$499$	4.59453	+	7.95797i	0.205680	+	0.356247i	0.950349	−	0.311186i	$-0.100726\pi$
$499$	4.59453	+	7.95797i	0.205680	+	0.356247i	−0.744669	+	0.667433i	$0.767393\pi$
$500$	−4.79850	+	8.31125i	−0.214595	+	0.371690i
$501$	60.2871			2.69343
$502$	12.3878			0.552895
$503$	3.61470	−	6.26085i	0.161172	−	0.279158i	−0.774117	−	0.633042i	$-0.781806\pi$
$503$	3.61470	−	6.26085i	0.161172	−	0.279158i	0.935289	+	0.353884i	$0.115139\pi$
$504$	14.6402	−	25.3576i	0.652127	−	1.12952i
$505$	1.32612			0.0590117
$506$	4.55291			0.202401
$507$	3.32432	−	5.75789i	0.147638	−	0.255717i
$508$	8.19303	+	14.1907i	0.363507	+	0.629612i
$509$	18.4552	−	31.9653i	0.818012	−	1.41684i	−0.0891335	−	0.996020i	$-0.528410\pi$
$509$	18.4552	−	31.9653i	0.818012	−	1.41684i	0.907145	−	0.420818i	$-0.138257\pi$
$510$	−5.28866	−	9.16023i	−0.234186	−	0.405622i
$511$	7.62808	+	13.2122i	0.337446	+	0.584474i
$512$	15.3035			0.676327
$513$	63.3285	+	18.2235i	2.79602	+	0.804588i
$514$	24.8823			1.09751
$515$	−9.88445	−	17.1204i	−0.435561	−	0.754414i
$516$	−0.570697	−	0.988476i	−0.0251235	−	0.0435152i
$517$	3.96958	−	6.87551i	0.174582	−	0.302385i
$518$	3.37923	+	5.85300i	0.148475	+	0.257166i
$519$	8.37427	−	14.5047i	0.367589	−	0.636684i
$520$	−15.3551			−0.673367
$521$	−4.73460			−0.207427			−0.103713	−	0.994607i	$-0.533072\pi$
$521$	−4.73460			−0.207427			−0.103713	+	0.994607i	$0.533072\pi$
$522$	−13.3486	+	23.1204i	−0.584252	+	1.01195i
$523$	9.02073	−	15.6244i	0.394449	−	0.683206i	−0.598582	−	0.801062i	$-0.704269\pi$
$523$	9.02073	−	15.6244i	0.394449	−	0.683206i	0.993031	+	0.117856i	$0.0376022\pi$
$524$	−12.0882			−0.528075
$525$	−13.5904			−0.593135
$526$	0.137800	−	0.238677i	0.00600837	−	0.0104068i
$527$	−9.89762	−	17.1432i	−0.431147	−	0.746768i
$528$	2.33895	−	4.05118i	0.101790	−	0.176305i
$529$	2.17705	+	3.77077i	0.0946545	+	0.163946i
$530$	−2.09882	−	3.63527i	−0.0911671	−	0.157906i
$531$	−37.7928			−1.64007
$532$	3.51032	−	3.38351i	0.152192	−	0.146694i
$533$	35.4531			1.53564
$534$	−23.5452	−	40.7815i	−1.01890	−	1.76479i
$535$	6.26120	+	10.8447i	0.270695	+	0.468858i
$536$	−17.5559	+	30.4077i	−0.758298	+	1.31341i
$537$	23.6355	+	40.9379i	1.01995	+	1.76660i
$538$	6.20152	−	10.7413i	0.267367	−	0.463092i
$539$	5.41444			0.233216
$540$	17.4606			0.751386
$541$	16.3726	−	28.3582i	0.703914	−	1.21922i	−0.263168	−	0.964750i	$-0.584767\pi$
$541$	16.3726	−	28.3582i	0.703914	−	1.21922i	0.967082	−	0.254465i	$-0.0818994\pi$
$542$	−14.0283	+	24.2977i	−0.602565	+	1.04367i
$543$	21.5552			0.925023
$544$	−10.8315			−0.464397
$545$	4.16271	−	7.21002i	0.178311	−	0.308843i
$546$	−8.39551	−	14.5414i	−0.359295	−	0.622316i
$547$	−13.4885	+	23.3628i	−0.576727	+	0.998920i	0.419125	+	0.907928i	$0.362337\pi$
$547$	−13.4885	+	23.3628i	−0.576727	+	0.998920i	−0.995852	+	0.0909912i	$0.970996\pi$
$548$	5.05510	+	8.75570i	0.215943	+	0.374025i
$549$	20.1649	+	34.9266i	0.860616	+	1.49063i
$550$	−3.48944			−0.148790
$551$	−10.4070	+	10.0310i	−0.443351	+	0.427336i
$552$	−42.8856			−1.82533
$553$	5.13753	+	8.89847i	0.218470	+	0.378401i
$554$	6.16432	+	10.6769i	0.261897	+	0.453618i
$555$	−10.7925	+	18.6932i	−0.458117	+	0.793482i
$556$	−2.98460	−	5.16947i	−0.126575	−	0.219235i
$557$	−2.74121	+	4.74791i	−0.116149	+	0.201175i	−0.918238	−	0.396028i	$-0.870388\pi$
$557$	−2.74121	+	4.74791i	−0.116149	+	0.201175i	0.802090	+	0.597204i	$0.203722\pi$
$558$	−67.3631			−2.85171
$559$	−1.52794			−0.0646250
$560$	−1.17420	+	2.03377i	−0.0496189	+	0.0859425i
$561$	−3.85778	+	6.68187i	−0.162875	+	0.282109i
$562$	−22.5142			−0.949705
$563$	21.3497			0.899784			0.449892	−	0.893083i	$-0.351463\pi$
$563$	21.3497			0.899784			0.449892	+	0.893083i	$0.351463\pi$
$564$	−11.4995	+	19.9177i	−0.484215	+	0.838685i
$565$	−2.23152	−	3.86511i	−0.0938807	−	0.162606i
$566$	−6.63829	+	11.4979i	−0.279028	+	0.483291i
$567$	16.6193	+	28.7854i	0.697944	+	1.20887i
$568$	9.48545	+	16.4293i	0.398000	+	0.689357i
$569$	−46.7817			−1.96119			−0.980596	−	0.196040i	$-0.937192\pi$
$569$	−46.7817			−1.96119			−0.980596	+	0.196040i	$0.937192\pi$
$570$	−18.7281	−	5.38922i	−0.784433	−	0.225730i
$571$	−11.2018			−0.468780			−0.234390	−	0.972143i	$-0.575309\pi$
$571$	−11.2018			−0.468780			−0.234390	+	0.972143i	$0.575309\pi$
$572$	1.72237	+	2.98323i	0.0720158	+	0.124735i
$573$	8.04183	+	13.9289i	0.335952	+	0.581887i
$574$	6.06888	−	10.5116i	0.253310	−	0.438746i
$575$	7.14529	+	12.3760i	0.297979	+	0.516115i
$576$	−29.3824	+	50.8917i	−1.22427	+	2.12049i
$577$	−25.5689			−1.06445			−0.532224	−	0.846603i	$-0.678644\pi$
$577$	−25.5689			−1.06445			−0.532224	+	0.846603i	$0.678644\pi$
$578$	12.0229			0.500088
$579$	8.85376	−	15.3352i	0.367950	−	0.637307i
$580$	−1.91493	+	3.31675i	−0.0795130	+	0.137720i
$581$	−5.35453			−0.222143
$582$	51.4879			2.13424
$583$	−1.53097	+	2.65172i	−0.0634064	+	0.109823i
$584$	−18.4485	−	31.9537i	−0.763403	−	1.32225i
$585$	19.2502	−	33.3423i	0.795897	−	1.37853i
$586$	−6.98722	−	12.1022i	−0.288639	−	0.499938i
$587$	−12.7122	−	22.0182i	−0.524690	−	0.908790i	−0.999587	−	0.0287484i	$-0.990848\pi$
$587$	−12.7122	−	22.0182i	−0.524690	−	0.908790i	0.474896	−	0.880042i	$-0.342486\pi$
$588$	−15.6851			−0.646842
$589$	−35.0492	−	10.0858i	−1.44418	−	0.415579i
$590$	6.78531			0.279347
$591$	6.24711	+	10.8203i	0.256972	+	0.445088i
$592$	−3.65087	−	6.32349i	−0.150050	−	0.259894i
$593$	−10.0063	+	17.3314i	−0.410909	+	0.711716i	−0.994989	−	0.0999802i	$-0.968122\pi$
$593$	−10.0063	+	17.3314i	−0.410909	+	0.711716i	0.584080	+	0.811696i	$0.301455\pi$
$594$	7.97012	+	13.8047i	0.327018	+	0.566412i
$595$	1.93668	−	3.35442i	0.0793961	−	0.137518i
$596$	21.0217			0.861082
$597$	58.4918			2.39391
$598$	−8.82803	+	15.2906i	−0.361005	+	0.625279i
$599$	−3.33024	+	5.76814i	−0.136070	+	0.235680i	−0.926006	−	0.377510i	$-0.876781\pi$
$599$	−3.33024	+	5.76814i	−0.136070	+	0.235680i	0.789936	+	0.613190i	$0.210114\pi$
$600$	32.8684			1.34185
$601$	9.58212			0.390863			0.195432	−	0.980717i	$-0.437389\pi$
$601$	9.58212			0.390863			0.195432	+	0.980717i	$0.437389\pi$
$602$	−0.261554	+	0.453024i	−0.0106601	+	0.0184639i
$603$	−44.0184	−	76.2421i	−1.79257	−	3.10482i
$604$	−8.04823	+	13.9399i	−0.327478	+	0.567208i
$605$	−0.650102	−	1.12601i	−0.0264304	−	0.0457788i
$606$	−1.75357	−	3.03727i	−0.0712338	−	0.123381i
$607$	−44.2594			−1.79643			−0.898217	−	0.439552i	$-0.855137\pi$
$607$	−44.2594			−1.79643			−0.898217	+	0.439552i	$0.855137\pi$
$608$	−14.3684	+	13.8494i	−0.582716	+	0.561666i
$609$	−13.6174			−0.551805
$610$	−3.62040	−	6.27071i	−0.146586	−	0.253894i
$611$	15.3939	+	26.6630i	0.622771	+	1.07867i
$612$	8.02331	−	13.8968i	0.324323	−	0.561744i
$613$	−19.1831	−	33.2261i	−0.774797	−	1.34199i	−0.934909	−	0.354889i	$-0.884519\pi$
$613$	−19.1831	−	33.2261i	−0.774797	−	1.34199i	0.160112	−	0.987099i	$-0.448815\pi$
$614$	0.649738	−	1.12538i	0.0262213	−	0.0454166i
$615$	38.7653			1.56317
$616$	3.83468			0.154504
$617$	−0.750993	+	1.30076i	−0.0302338	+	0.0523666i	−0.880746	−	0.473588i	$-0.842959\pi$
$617$	−0.750993	+	1.30076i	−0.0302338	+	0.0523666i	0.850513	+	0.525955i	$0.176292\pi$
$618$	−26.1410	+	45.2775i	−1.05154	+	1.82133i
$619$	−6.81874			−0.274068			−0.137034	−	0.990566i	$-0.543757\pi$
$619$	−6.81874			−0.274068			−0.137034	+	0.990566i	$0.543757\pi$
$620$	−9.66359			−0.388099
$621$	32.6407	−	56.5353i	1.30983	−	2.26868i
$622$	9.20408	+	15.9419i	0.369050	+	0.639213i
$623$	8.62213	−	14.9340i	0.345438	−	0.598317i
$624$	9.07039	+	15.7104i	0.363106	+	0.628918i
$625$	−1.24997	−	2.16501i	−0.0499988	−	0.0866004i
$626$	−28.5881			−1.14261
$627$	3.42607	+	13.7964i	0.136824	+	0.550975i
$628$	5.45957			0.217861
$629$	6.02161	+	10.4297i	0.240097	+	0.415861i
$630$	−6.59051	−	11.4151i	−0.262572	−	0.454789i
$631$	3.98717	−	6.90598i	0.158727	−	0.274923i	−0.775683	−	0.631123i	$-0.782594\pi$
$631$	3.98717	−	6.90598i	0.158727	−	0.274923i	0.934410	+	0.356200i	$0.115928\pi$
$632$	−12.4251	−	21.5209i	−0.494244	−	0.856055i
$633$	−4.78609	+	8.28975i	−0.190230	+	0.329488i
$634$	13.0381			0.517810
$635$	23.9848			0.951806
$636$	4.43507	−	7.68177i	0.175862	−	0.304602i
$637$	−10.4985	+	18.1840i	−0.415967	+	0.720475i
$638$	−3.49637			−0.138422
$639$	−47.5663			−1.88169
$640$	−0.677426	+	1.17334i	−0.0267776	+	0.0463802i
$641$	15.4787	+	26.8100i	0.611374	+	1.05893i	0.991009	+	0.133794i	$0.0427160\pi$
$641$	15.4787	+	26.8100i	0.611374	+	1.05893i	−0.379636	+	0.925136i	$0.623951\pi$
$642$	16.5587	−	28.6805i	0.653520	−	1.13193i
$643$	15.6354	+	27.0813i	0.616599	+	1.06798i	0.990102	+	0.140351i	$0.0448232\pi$
$643$	15.6354	+	27.0813i	0.616599	+	1.06798i	−0.373503	+	0.927629i	$0.621843\pi$
$644$	−2.41493	−	4.18278i	−0.0951615	−	0.164825i
$645$	−1.67069			−0.0657834
$646$	−7.82863	+	7.54583i	−0.308013	+	0.296887i
$647$	−1.49893			−0.0589289			−0.0294644	−	0.999566i	$-0.509380\pi$
$647$	−1.49893			−0.0589289			−0.0294644	+	0.999566i	$0.509380\pi$
$648$	−40.1936	−	69.6174i	−1.57895	−	2.73483i
$649$	−2.47475	−	4.28639i	−0.0971424	−	0.168256i
$650$	6.76598	−	11.7190i	0.265384	−	0.459658i
$651$	−17.1799	−	29.7565i	−0.673334	−	1.16625i
$652$	−0.739377	+	1.28064i	−0.0289562	+	0.0501537i
$653$	−2.66211			−0.104176			−0.0520881	−	0.998642i	$-0.516588\pi$
$653$	−2.66211			−0.104176			−0.0520881	+	0.998642i	$0.516588\pi$
$654$	−22.0178			−0.860965
$655$	−8.84692	+	15.3233i	−0.345678	+	0.598732i
$656$	−6.55672	+	11.3566i	−0.255997	+	0.443400i
$657$	92.5129			3.60927
$658$	10.5406			0.410913
$659$	10.2629	−	17.7759i	0.399787	−	0.692451i	−0.593912	−	0.804530i	$-0.702417\pi$
$659$	10.2629	−	17.7759i	0.399787	−	0.692451i	0.993699	+	0.112078i	$0.0357508\pi$
$660$	1.88328	+	3.26194i	0.0733066	+	0.126971i
$661$	18.1293	−	31.4009i	0.705148	−	1.22135i	−0.261490	−	0.965206i	$-0.584214\pi$
$661$	18.1293	−	31.4009i	0.705148	−	1.22135i	0.966638	−	0.256146i	$-0.0824528\pi$
$662$	18.2706	+	31.6455i	0.710106	+	1.22994i
$663$	−14.9604	−	25.9121i	−0.581012	−	1.00634i
$664$	12.9499			0.502554
$665$	−1.71995	−	6.92605i	−0.0666969	−	0.268581i
$666$	40.9831			1.58806
$667$	7.15948	+	12.4006i	0.277216	+	0.480152i
$668$	−8.21036	−	14.2208i	−0.317669	−	0.550218i
$669$	−11.8295	+	20.4893i	−0.457354	+	0.792161i
$670$	7.90304	+	13.6885i	0.305321	+	0.528832i
$671$	−2.64087	+	4.57412i	−0.101950	+	0.176582i
$672$	−18.8009			−0.725261
$673$	−36.7230			−1.41557			−0.707783	−	0.706430i	$-0.750305\pi$
$673$	−36.7230			−1.41557			−0.707783	+	0.706430i	$0.750305\pi$
$674$	−5.94743	+	10.3013i	−0.229087	+	0.396790i
$675$	−25.0165	+	43.3298i	−0.962885	+	1.66776i
$676$	−1.81093			−0.0696510
$677$	−5.17724			−0.198977			−0.0994887	−	0.995039i	$-0.531721\pi$
$677$	−5.17724			−0.198977			−0.0994887	+	0.995039i	$0.531721\pi$
$678$	−5.90160	+	10.2219i	−0.226649	+	0.392568i
$679$	9.42728	+	16.3285i	0.361786	+	0.626631i
$680$	−4.68385	+	8.11266i	−0.179617	+	0.311106i
$681$	25.1020	+	43.4780i	0.961911	+	1.66608i
$682$	−4.41107	−	7.64020i	−0.168909	−	0.292558i
$683$	−37.2094			−1.42378			−0.711889	−	0.702292i	$-0.752160\pi$
$683$	−37.2094			−1.42378			−0.711889	+	0.702292i	$0.752160\pi$
$684$	−7.12545	−	28.6934i	−0.272449	−	1.09712i
$685$	14.7986			0.565426
$686$	8.24112	+	14.2740i	0.314647	+	0.544985i
$687$	8.61301	+	14.9182i	0.328607	+	0.569164i
$688$	0.282579	−	0.489441i	0.0107732	−	0.0186598i
$689$	−5.93707	−	10.2833i	−0.226184	−	0.391763i
$690$	−9.65280	+	16.7191i	−0.367476	+	0.636487i
$691$	−12.0273			−0.457539			−0.228769	−	0.973481i	$-0.573470\pi$
$691$	−12.0273			−0.457539			−0.228769	+	0.973481i	$0.573470\pi$
$692$	−4.56189			−0.173417
$693$	−4.80740	+	8.32666i	−0.182618	+	0.316304i
$694$	3.83575	−	6.64371i	0.145603	−	0.252192i
$695$	−8.73728			−0.331424
$696$	32.9336			1.24835
$697$	10.8144	−	18.7311i	0.409625	−	0.709492i
$698$	12.8088	+	22.1854i	0.484819	+	0.839732i
$699$	−33.7266	+	58.4162i	−1.27566	+	2.20950i
$700$	1.85085	+	3.20576i	0.0699555	+	0.121166i
$701$	−12.7683	−	22.1154i	−0.482252	−	0.835286i	0.517540	−	0.855659i	$-0.326848\pi$
$701$	−12.7683	−	22.1154i	−0.482252	−	0.835286i	−0.999792	+	0.0203733i	$0.993515\pi$
$702$	−61.8159			−2.33309
$703$	21.3236	+	6.13611i	0.804233	+	0.231428i
$704$	−7.69606			−0.290056
$705$	16.8321	+	29.1541i	0.633934	+	1.09801i
$706$	−15.2484	−	26.4109i	−0.573880	−	0.993989i
$707$	0.642147	−	1.11223i	0.0241504	−	0.0418297i
$708$	7.16910	+	12.4172i	0.269431	+	0.466669i
$709$	−0.336850	+	0.583442i	−0.0126507	+	0.0219116i	−0.872281	−	0.489004i	$-0.837360\pi$
$709$	−0.336850	+	0.583442i	−0.0126507	+	0.0219116i	0.859631	+	0.510916i	$0.170694\pi$
$710$	8.54004			0.320502
$711$	62.3076			2.33672
$712$	−20.8526	+	36.1177i	−0.781483	+	1.35357i
$713$	−18.0650	+	31.2895i	−0.676540	+	1.17180i
$714$	−10.2437			−0.383360
$715$	5.04216			0.188566
$716$	6.43773	−	11.1505i	0.240589	−	0.416713i
$717$	−28.9142	−	50.0808i	−1.07982	−	1.87030i
$718$	10.0648	−	17.4328i	0.375615	−	0.650585i
$719$	−5.61360	−	9.72304i	−0.209352	−	0.362608i	0.742159	−	0.670224i	$-0.233802\pi$
$719$	−5.61360	−	9.72304i	−0.209352	−	0.362608i	−0.951511	+	0.307616i	$0.900469\pi$
$720$	7.12029	+	12.3327i	0.265358	+	0.459613i
$721$	−19.1453			−0.713009
$722$	−0.736743	+	20.0197i	−0.0274187	+	0.745055i
$723$	45.6444			1.69753
$724$	−2.93555	−	5.08453i	−0.109099	−	0.188965i
$725$	−5.48717	−	9.50405i	−0.203788	−	0.352972i
$726$	−1.71929	+	2.97791i	−0.0638090	+	0.110520i
$727$	7.48464	+	12.9638i	0.277590	+	0.480800i	0.970785	−	0.239950i	$-0.0771310\pi$
$727$	7.48464	+	12.9638i	0.277590	+	0.480800i	−0.693195	+	0.720750i	$0.743798\pi$
$728$	−7.43539	+	12.8785i	−0.275574	+	0.477308i
$729$	53.6460			1.98689
$730$	−16.6097			−0.614753
$731$	−0.466075	+	0.807266i	−0.0172384	+	0.0298578i
$732$	7.65034	−	13.2508i	0.282765	−	0.489763i
$733$	−13.8590			−0.511895			−0.255947	−	0.966691i	$-0.582387\pi$
$733$	−13.8590			−0.511895			−0.255947	+	0.966691i	$0.582387\pi$
$734$	23.4322			0.864900
$735$	−11.4794	+	19.8828i	−0.423423	+	0.733389i
$736$	9.88476	+	17.1209i	0.364357	+	0.631085i
$737$	5.76482	−	9.98495i	0.212350	−	0.367801i
$738$	−36.8015	−	63.7420i	−1.35468	−	2.34637i
$739$	22.8411	+	39.5620i	0.840224	+	1.45531i	0.889705	+	0.456536i	$0.150910\pi$
$739$	22.8411	+	39.5620i	0.840224	+	1.45531i	−0.0494812	+	0.998775i	$0.515757\pi$
$740$	5.87923			0.216125
$741$	−52.9772	−	15.2448i	−1.94617	−	0.560032i
$742$	−4.06524			−0.149240
$743$	−13.6125	−	23.5776i	−0.499394	−	0.864977i	0.500605	−	0.865676i	$-0.333111\pi$
$743$	−13.6125	−	23.5776i	−0.499394	−	0.864977i	−1.00000		0.000699114i	$0.999777\pi$
$744$	41.5495	+	71.9659i	1.52328	+	2.63840i
$745$	15.3850	−	26.6476i	0.563664	−	0.976294i
$746$	−10.7247	−	18.5757i	−0.392659	−	0.680106i
$747$	−16.2348	+	28.1196i	−0.594002	+	1.02884i
$748$	2.10153			0.0768394
$749$	12.1274			0.443126
$750$	18.5753	−	32.1733i	0.678273	−	1.17480i
$751$	9.07155	−	15.7124i	0.331026	−	0.573353i	−0.651688	−	0.758487i	$-0.725939\pi$
$751$	9.07155	−	15.7124i	0.331026	−	0.573353i	0.982713	+	0.185134i	$0.0592720\pi$
$752$	−11.3879			−0.415272
$753$	38.3160			1.39631
$754$	6.77941	−	11.7423i	0.246892	−	0.427629i
$755$	11.7804	+	20.4043i	0.428734	+	0.742588i
$756$	8.45493	−	14.6444i	0.307503	−	0.532611i
$757$	8.78303	+	15.2127i	0.319225	+	0.552913i	0.980326	−	0.197383i	$-0.0632442\pi$
$757$	8.78303	+	15.2127i	0.319225	+	0.552913i	−0.661102	+	0.750296i	$0.729911\pi$
$758$	9.20540	+	15.9442i	0.334355	+	0.579120i
$759$	14.0823			0.511156
$760$	4.15970	+	16.7506i	0.150888	+	0.607609i
$761$	26.9682			0.977597			0.488798	−	0.872397i	$-0.337435\pi$
$761$	26.9682			0.977597			0.488798	+	0.872397i	$0.337435\pi$
$762$	−31.7157	−	54.9332i	−1.14894	−	1.99002i
$763$	−4.03140	−	6.98259i	−0.145947	−	0.252787i
$764$	2.19040	−	3.79388i	0.0792458	−	0.137258i
$765$	−11.7440	−	20.3411i	−0.424603	−	0.735435i
$766$	−1.30056	+	2.25264i	−0.0469911	+	0.0813910i
$767$	19.1940			0.693056
$768$	53.7805			1.94064
$769$	15.7719	−	27.3178i	0.568750	−	0.985105i	−0.427939	−	0.903807i	$-0.640760\pi$
$769$	15.7719	−	27.3178i	0.568750	−	0.985105i	0.996690	−	0.0812973i	$-0.0259063\pi$
$770$	0.863119	−	1.49497i	0.0311046	−	0.0538748i
$771$	76.9621

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.527190 + 0.913120i) q^{2} +(1.63062 + 2.82432i) q^{3} +(0.444141 - 0.769275i) q^{4} +(-0.650102 - 1.12601i) q^{5} +(-1.71929 + 2.97791i) q^{6} -1.25919 q^{7} +3.04535 q^{8} +(-3.81785 + 6.61271i) q^{9} +O(q^{10})\)	\(q+(0.527190 + 0.913120i) q^{2} +(1.63062 + 2.82432i) q^{3} +(0.444141 - 0.769275i) q^{4} +(-0.650102 - 1.12601i) q^{5} +(-1.71929 + 2.97791i) q^{6} -1.25919 q^{7} +3.04535 q^{8} +(-3.81785 + 6.61271i) q^{9} +(0.685455 - 1.18724i) q^{10} -1.00000 q^{11} +2.89690 q^{12} +(1.93899 - 3.35842i) q^{13} +(-0.663833 - 1.14979i) q^{14} +(2.12014 - 3.67219i) q^{15} +(0.717196 + 1.24222i) q^{16} +(-1.18292 - 2.04887i) q^{17} -8.05093 q^{18} +(-4.18891 - 1.20541i) q^{19} -1.15495 q^{20} +(-2.05326 - 3.55636i) q^{21} +(-0.527190 - 0.913120i) q^{22} +(-2.15904 + 3.73957i) q^{23} +(4.96581 + 8.60103i) q^{24} +(1.65473 - 2.86608i) q^{25} +4.08886 q^{26} -15.1181 q^{27} +(-0.559258 + 0.968664i) q^{28} +(1.65802 - 2.87177i) q^{29} +4.47087 q^{30} +8.36713 q^{31} +(2.28915 - 3.96492i) q^{32} +(-1.63062 - 2.82432i) q^{33} +(1.24724 - 2.16029i) q^{34} +(0.818603 + 1.41786i) q^{35} +(3.39132 + 5.87395i) q^{36} -5.09048 q^{37} +(-1.10767 - 4.46046i) q^{38} +12.6470 q^{39} +(-1.97979 - 3.42909i) q^{40} +(4.57108 + 7.91735i) q^{41} +(2.16492 - 3.74975i) q^{42} +(-0.197002 - 0.341218i) q^{43} +(-0.444141 + 0.769275i) q^{44} +9.92796 q^{45} -4.55291 q^{46} +(-3.96958 + 6.87551i) q^{47} +(-2.33895 + 4.05118i) q^{48} -5.41444 q^{49} +3.48944 q^{50} +(3.85778 - 6.68187i) q^{51} +(-1.72237 - 2.98323i) q^{52} +(1.53097 - 2.65172i) q^{53} +(-7.97012 - 13.8047i) q^{54} +(0.650102 + 1.12601i) q^{55} -3.83468 q^{56} +(-3.42607 - 13.7964i) q^{57} +3.49637 q^{58} +(2.47475 + 4.28639i) q^{59} +(-1.88328 - 3.26194i) q^{60} +(2.64087 - 4.57412i) q^{61} +(4.41107 + 7.64020i) q^{62} +(4.80740 - 8.32666i) q^{63} +7.69606 q^{64} -5.04216 q^{65} +(1.71929 - 2.97791i) q^{66} +(-5.76482 + 9.98495i) q^{67} -2.10153 q^{68} -14.0823 q^{69} +(-0.863119 + 1.49497i) q^{70} +(3.11473 + 5.39488i) q^{71} +(-11.6267 + 20.1380i) q^{72} +(-6.05792 - 10.4926i) q^{73} +(-2.68365 - 4.64822i) q^{74} +10.7930 q^{75} +(-2.78776 + 2.68705i) q^{76} +1.25919 q^{77} +(6.66738 + 11.5482i) q^{78} +(-4.08003 - 7.06681i) q^{79} +(0.932501 - 1.61514i) q^{80} +(-13.1984 - 22.8602i) q^{81} +(-4.81966 + 8.34790i) q^{82} +4.25236 q^{83} -3.64775 q^{84} +(-1.53803 + 2.66395i) q^{85} +(0.207716 - 0.359774i) q^{86} +10.8144 q^{87} -3.04535 q^{88} +(-6.84735 + 11.8600i) q^{89} +(5.23392 + 9.06542i) q^{90} +(-2.44156 + 4.22890i) q^{91} +(1.91784 + 3.32180i) q^{92} +(13.6436 + 23.6314i) q^{93} -8.37089 q^{94} +(1.36592 + 5.50039i) q^{95} +14.9309 q^{96} +(-7.48677 - 12.9675i) q^{97} +(-2.85444 - 4.94403i) q^{98} +(3.81785 - 6.61271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9}+O(q^{10}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9} + 21 q^{10} - 18 q^{11} + 16 q^{12} + 11 q^{13} + q^{14} + 7 q^{15} - 13 q^{16} + 6 q^{17} - 8 q^{18} + 4 q^{19} + 4 q^{20} + 24 q^{21} - q^{22} - q^{23} - 3 q^{24} - 7 q^{25} - 4 q^{26} + 6 q^{27} - 2 q^{28} + 13 q^{29} - 64 q^{30} - 32 q^{31} - 14 q^{32} + 8 q^{34} - 12 q^{35} + 10 q^{36} - 36 q^{37} - 20 q^{38} + 20 q^{39} + 32 q^{40} + 4 q^{41} + 11 q^{42} + q^{43} + 9 q^{44} + 22 q^{45} - 14 q^{46} - 14 q^{47} + 37 q^{48} - 12 q^{49} + 30 q^{50} - 16 q^{51} + 57 q^{52} - 4 q^{53} - 33 q^{54} - 34 q^{56} - 7 q^{57} + 8 q^{58} + 31 q^{59} + 9 q^{60} + 3 q^{61} + 5 q^{62} + 50 q^{63} + 64 q^{64} - 56 q^{65} + 3 q^{66} - 2 q^{67} - 96 q^{68} - 58 q^{70} - 12 q^{71} + 5 q^{72} - 26 q^{73} + 35 q^{74} + 50 q^{75} - 36 q^{76} + 6 q^{77} + 3 q^{78} + 31 q^{79} + 31 q^{80} - 21 q^{81} + 25 q^{82} + 36 q^{83} - 102 q^{84} - 11 q^{85} + 41 q^{86} - 124 q^{87} - 11 q^{89} + 51 q^{90} - 20 q^{91} - 33 q^{92} + 20 q^{93} - 86 q^{94} + 17 q^{95} + 60 q^{96} + 16 q^{97} + 4 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9 + 21 * q^10 - 18 * q^11 + 16 * q^12 + 11 * q^13 + q^14 + 7 * q^15 - 13 * q^16 + 6 * q^17 - 8 * q^18 + 4 * q^19 + 4 * q^20 + 24 * q^21 - q^22 - q^23 - 3 * q^24 - 7 * q^25 - 4 * q^26 + 6 * q^27 - 2 * q^28 + 13 * q^29 - 64 * q^30 - 32 * q^31 - 14 * q^32 + 8 * q^34 - 12 * q^35 + 10 * q^36 - 36 * q^37 - 20 * q^38 + 20 * q^39 + 32 * q^40 + 4 * q^41 + 11 * q^42 + q^43 + 9 * q^44 + 22 * q^45 - 14 * q^46 - 14 * q^47 + 37 * q^48 - 12 * q^49 + 30 * q^50 - 16 * q^51 + 57 * q^52 - 4 * q^53 - 33 * q^54 - 34 * q^56 - 7 * q^57 + 8 * q^58 + 31 * q^59 + 9 * q^60 + 3 * q^61 + 5 * q^62 + 50 * q^63 + 64 * q^64 - 56 * q^65 + 3 * q^66 - 2 * q^67 - 96 * q^68 - 58 * q^70 - 12 * q^71 + 5 * q^72 - 26 * q^73 + 35 * q^74 + 50 * q^75 - 36 * q^76 + 6 * q^77 + 3 * q^78 + 31 * q^79 + 31 * q^80 - 21 * q^81 + 25 * q^82 + 36 * q^83 - 102 * q^84 - 11 * q^85 + 41 * q^86 - 124 * q^87 - 11 * q^89 + 51 * q^90 - 20 * q^91 - 33 * q^92 + 20 * q^93 - 86 * q^94 + 17 * q^95 + 60 * q^96 + 16 * q^97 + 4 * q^98 + 11 * q^99

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